Marco Benini

Mathematical Logic

  • Propositional logic: language, deduction system, semantics, soundness, completeness;
  • First-order logic: syntax, semantics, soundness, completeness, compactness;
  • Set theory: fundamental axioms, ordinals, cardinals, transfinite induction, axiom of choice, continuum hypothesis;
  • Computability: computable functions, λ-calculi, simple theory of types;
  • Constructive mathematics: intuitionistic logic, propositions as types, normalisation;
  • Limiting results: Peano arithmetic, Gödel’s incompleteness theorems, natural incompleteness results.

The slides of the course are available: select the right academic year

Here are some exercises on natural deduction.
The official online course is available: please carefully read the introductory notes!

The non-official videos are available in the video page.
Note that this course on YouTube differs from the online course!

7 nov 2016pdfpdf
5 dec 2016pdfpdf
16/17 jan 2017pdfpdf
1 feb 2017pdfpdf
23 mar 2018pdfpdf
2 may 2018pdfpdf
25 may 2018pdfpdf
8 jun 2018pdfpdf
31 oct 2018pdfpdf
28 nov 2018pdfpdf
10 jan 2019pdfpdf
5 feb 2019pdfpdf
24 oct 2019pdfpdf
27 nov 2019pdfpdf
10 jan 2020pdfpdf
28 jan 2020pdfpdf
9 apr 2021pdfpdf
30 apr 2021pdfpdf
28 may 2021pdfpdf
15 june 2021pdfpdf


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